z varies jointly with y and the square of x. If z=256 when y=-8 and x=-4, find z when x=-3 and y=-4.
z = k y x^2
256 = k (-8)(16)
k = 256 / -128 = -2
so
z = -2 y x^2
= -2 * -3 * 16
z=ky*x^2
256=k(-8)(4)^2 solve for k.
then find z when x=-3, y=-4. K is a constant, and does not change.
whoops -2 * -4 * 9
z = kyx^2
That is,
z/(yx^2) = k, a constant. So, you want z such that
z/(-4*9) = 256/(-8*16)
To solve this problem, we can set up the joint variation equation. The equation for joint variation is given by:
z = k * x^2 * y
where z is the variable that varies jointly with y and the square of x, k is the constant of variation, x is one of the variables, and y is the other variable.
First, we need to find the value of k using the initial values of z, y, and x. We have:
256 = k * (-4)^2 * (-8)
Simplifying the equation:
256 = k * 16 * (-8)
256 = -128k
Solving for k:
k = 256 / -128
k = -2
Now that we have the value of k, we can use it to find the value of z when x = -3 and y = -4. Substituting the values into the joint variation equation:
z = (-2) * (-3)^2 * (-4)
z = (-2) * 9 * (-4)
z = 72
Therefore, when x = -3 and y = -4, z = 72.